Oops, sorry. I’d thought that tour bypassed Venice, but sure enough, 2 nights and parts of 3 days are there. The city definitely is among the best parts of Europe, so that makes sense to have it on the tour, but then more time in Venice is better than not enough time. If the flight and meet/up possibilities make sense for Venice, then you’ll all get double the experience.
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The tour doesn’t include the French Riviera, including Nice, another place that would be on many people’s “best” list. So fly in to Marseille or Nice, see some of the south of France, and then work your way down to Rome. It can take the better part of a whole day by train, but split that up over a couple days. Probably wind up connecting trains at Milan.
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Just fly to Milan to begin with. Make reservations ahead of time, and see Leonardo’s Last Supper, which now has limited admission to protect the fragile artwork. A truly spectacular cathedral in Italy’s second biggest city, and northern Italy has a different vibe than Rome or Florence. More Italy for your money.
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Just get to Rome early. We were there an entire week and still didn’t cover everything. Lots of museums, churches, and historical sights that the tour won’t cover, and that the free time on the tour won’t make available. Get some Rome under your belt that the tour can’t.